The Cauchy problem in 2D and 3D steady-state anisotropic heat conduction is investigated for both exact and perturbed data, i.e. the numerical reconstruction of the missing temperature and normal heat flux on a part of the boundary from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary. This inverse Cauchy problem is solved by applying and adapting the fading regularization method, proposed by Cimetière et al. [7, 8] for the steady-state isotropic heat conduction, to the anisotropic case. An appropriate stabilizing/regularizing stopping criterion for the resulting iterative algorithm is provided for each type of Cauchy data considered. The numerical implementation is realized for 2D and 3D homogeneous solids by using the meshless method of fundamental solutions.

针对精确和扰动数据研究了 2D 和 3D 稳态各向异性热传导中的柯西问题，即根据精确或嘈杂的柯西数据对边界部分缺失温度和法向热通量的数值重建剩余的和可访问的边界。这个逆柯西问题是通过应用和调整 Cimetière 等人提出的衰落正则化方法来解决的。[7, 8] 为稳态各向同性热传导，为各向异性情况。为所考虑的每种类型的柯西数据提供了用于最终迭代算法的适当的稳定/正则化停止标准。通过使用基本解的无网格方法实现了 2D 和 3D 均匀实体的数值实现。